Question

if the perimeter of a square increases of 25%,what is the increase in its area???

Answer 1

hi...hi... 
if \:perimeter \: is \: 1ifperimeteris1 
We know that ,

Perimeter = 4(side)

1 = 4(side)

side = 1 / 4

Area = side × side
Area = 1 / 4 × 1 / 4
Area = 1 / 16 sq . cm

if \: perimeter \: is \: 2ifperimeteris2 
Perimeter = 4(side)
2 = 4(side)
1 = 2(side)
side = 1 / 2

Area = side × side 
Area = 1 / 2 × 1 /2 
Area = 1 / 4

Percent increased 
= 1 / 16 ÷ 1 / 4 × 25
= 1 / 16 × 4 × 25
= 100 / 16
= 25 / 4 %
hope \: \: this \: \: helps..hopethishelps.. 

Answer 2

Let the side of square be x.

Perimeter of square = 4x

Increase in perimeter = 25% of 4x

$= \frac{25}{100} \times 4x \\ \\ = \frac{100x}{100} \\ \\ = x$


New perimeter = 4x +x = 5x

Let the new side be y.

4y = 5x

$y = \frac{5}{4} x$
$old \: area = {x}^{2} \\ \\ new \: area \: = {y}^{2} \\ \\ = {( \frac{5}{4}x) }^{2} \\ \\ = \frac{25}{16} {x}^{2}$
Area increase = new area - old area

$= \frac{25}{16} {x}^{2} - {x}^{2} \\ \\ = {x}^{2} ( \frac{25}{16} - 1) \\ \\ = {x}^{2} ( \frac{25 - 16}{16} ) \\ \\ = {x}^{2} ( \frac{9}{4} ) \\ \\ = \frac{9}{4} times \: of \: old \: area$